Regular triangulations of the 3-dilated 3-simplex

You can find all regular triangulations of the 3-dilated 3-simplex here. There are 910,974,879 triangulations in total.

These output files were produced by mptopcom v1.0. The triangulations are denoted up to group action by the linear symmetry group on the simplex.

After extracting, every line in the output files corresponds to a triangulation orbit. E.g.:

> xzcat 3d3.result.000.xz |head
(0.0):[0->20,4:{{0,3,9,19}}]  gkz: [27,0,0,27,0,0,0,0,0,27,0,0,0,0,0,0,0,0,0,27] can(gkz): [27,0,0,27,0,0,0,0,0,27,0,0,0,0,0,0,0,0,0,27]
(2.0):[0->20,4:{{3,5,9,19},{0,5,9,19},{0,3,5,19}}]  gkz: [18,0,0,18,0,27,0,0,0,18,0,0,0,0,0,0,0,0,0,27] can(gkz): [27,0,0,18,0,0,0,0,0,18,0,0,0,0,27,0,0,0,0,18]
(2.1):[0->20,4:{{0,5,9,19},{5,9,17,19},{0,5,17,19},{3,5,9,17},{0,3,5,17}}]  gkz: [18,0,0,12,0,27,0,0,0,18,0,0,0,0,0,0,0,18,0,15] can(gkz): [18,0,0,18,0,27,0,0,0,12,0,0,0,0,0,0,0,0,18,15]

Every line contains three things: - A representative from the triangulation orbit in curly braces, - The gkz vector of this representative in square brackets after the gkz, - The lex largest gkz vector from this triangulation orbit in square brackets after the can(gkz). Note This is the old mptopcom format, the output format is changed in mptopcom v1.1.